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Research Papers

An Efficient Approach for Stability Analysis and Parameter Tuning in Delayed Feedback Control of a Flying Robot Carrying a Suspended Load

[+] Author and Article Information
Wei Dong

State Key Laboratory of
Mechanical System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: dr.dongwei@sjtu.edu.cn

Ye Ding

State Key Laboratory of
Mechanical System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: y.ding@sjtu.edu.cn

Luo Yang

State Key Laboratory of
Mechanical System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: yangluo@sjtu.edu.cn

Xinjun Sheng

State Key Laboratory of
Mechanical System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: xjsheng@sjtu.edu.cn

Xiangyang Zhu

State Key Laboratory of
Mechanical System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: mexyzhu@sjtu.edu.cn

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received January 30, 2018; final manuscript received March 7, 2019; published online April 9, 2019. Assoc. Editor: Jongeun Choi.

J. Dyn. Sys., Meas., Control 141(8), 081015 (Apr 09, 2019) (10 pages) Paper No: DS-18-1049; doi: 10.1115/1.4043223 History: Received January 30, 2018; Revised March 07, 2019

This paper presents an accurate and computationally efficient time-domain design method for the stability region determination and optimal parameter tuning of delayed feedback control of a flying robot carrying a suspended load. This work first utilizes a first-order time-delay (FOTD) equation to describe the performance of the flying robot, and the suspended load is treated as a flying pendulum. Thereafter, a typical delayed feedback controller is implemented, and the state-space equation of the whole system is derived and described as a periodic time-delay system. On this basis, the differential quadrature method is adopted to estimate the time-derivative of the state vector at concerned sampling grid point. In such a case, the transition matrix between adjacent time-delay duration can be obtained explicitly. The stability region of the feedback system is thereby within the unit circle of spectral radius of this transition matrix, and the minimum spectral radius within the unit circle guarantees fast tracking error decay. The proposed approach is also further illustrated to be able to be applied to some more sophisticated delayed feedback system, such as the input shaping with feedback control. To enhance the efficiency and robustness of parameter optimization, the derivatives of the spectral radius regarding the parameters are also presented explicitly. Finally, extensive numeric simulations and experiments are conducted to verify the effectiveness of the proposed method, and the results show that the proposed strategy efficiently estimates the optimal control parameters as well as the stability region. On this basis, the suspended load can effectively track the pre-assigned trajectory without large oscillations.

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Figures

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Fig. 1

The illustration of the suspended transportation with flying robot

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Fig. 2

The control structure of feedback control for the flying robot carrying a suspended load

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Fig. 3

Control structure of a typical input shaping with linear feedback

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Fig. 4

The contour plot of spectral radius regarding parameters h and Kp: (a) DQM and (b) LMI

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Fig. 5

The responses of different control strategies

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Fig. 6

The 3D plot of the ITAEC evaluation

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Fig. 7

The stability region investigation of system (27) with input shaper: (a) 3D stability region and (b) τs = 1.01

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Fig. 8

The gradient of the spectral radius

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Fig. 9

The response of delayed feedback control system with different parameters

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Fig. 10

The flying robot testbed utilized by this work

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Fig. 11

The real-time flight results of the open-loop transportation and delay feedback control: (a) normal and (b) delayed feedback control

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Fig. 12

The cross tracking error of the suspended load

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Fig. 13

The response of the suspended load with external disturbance

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